A mathematical model for determining the damping coefficient for structural materials

Abstract

At present, the effects of resonance in the coincidence of natural and forced vibrations of mechanical systems are not taken into account in the design of machines, mechanisms and building structures in most cases. These effects are strongly influenced by damping properties of structural materials. In this paper we propose a mathematical model for determining the damping properties of the material of an oscillating mechanical system, taking into account the (internal resistance) damping properties of the material. The main difficulty of this problem is the separation of the damping properties of the material from the general damping characteristics of the oscillating system (external environment, fixation, interaction of parts of the system with each other, etc.). The most obvious damping characteristics of materials are shown on the example of vibrations and their damping in the study of free vibrations of a beam with one degree of freedom (taking into account internal resistance). The proposed mathematical model allows to realise specific numerical solutions quite simply, and it also correlates well with the results of other studies, clarifying their results. The difference between the mathematical model proposed in this paper and the existing solutions is that the internal resistance of the oscillating system material is correctly taken into account.